Consistency of the LQG quantization of black holes coupled with scalar matter and a clock

TL;DR

This paper investigates the consistency of Loop Quantum Gravity's black hole quantization with scalar matter when using a gauge fixing approach with a physical clock, focusing on the outer black hole region.

Contribution

It analyzes the gauge-fixed quantization's ability to reproduce known vacuum black hole results in a more general outer region setting.

Findings

The gauge-fixed approach can reproduce vacuum black hole quantization results.

The analysis extends the validity of previous asymptotic approximations.

It addresses the constraint algebra consistency at the quantum level.

Abstract

The Dirac quantization of spherically symmetric gravity coupled to a scalar field in Loop Quantum Gravity remains unresolved, mainly because of the difficulty in maintaining a consistent constraint algebra at the quantum level. One possible way to overcome this obstruction is to fix the gauge by coupling the system to a physical clock. However, this approach requires careful control of the consistency of the gauge-fixed theory and factor-ordering ambiguities. Here, we address these issues by analyzing whether the gauge-fixed quantization reproduces the well-known results for the quantization of a black hole in vacuum using the Dirac method. This requires a treatment valid throughout the outer region of the black hole, where the asymptotic approximations considered in previous studies do not hold true.